In Exercises 57–64, factor using the formula for the sum or diffe...

Question

In Exercises 57–64, factor using the formula for the sum or difference of two cubes. x^3+64

Accepted Answer

Hello today we're going to be factoring a sum or difference of two cubed numbers. Now when we are factoring a summer difference we have to keep in mind that we have two general rules for factoring this. So we have the general rule for factoring of some of cubes which is a cubed plus B cubed. And that can be rewritten as a plus B times the quantity A squared minus A times B plus b squared. And we have the general rule for factoring a difference of cubes which is a cubed minus B cubed can be written as a minus B times the quantity A squared plus eight times B plus B squared. Now depending on what is given to you will tell you which role you need to use. However keep in mind that there is a difference in the pattern of signs for each for the sum of two cube numbers, the pattern is plus minus plus and for a difference of cubes the pattern would be minus plus plus. So the biggest difference between factory, a sum of cubes and a difference of cubes is the first two signs are always opposite of each other. For a for a sum we have plus and minus and for a difference we have minus and plus. So we just need to go ahead and keep that in mind. Let's go ahead and take a look at the expression given to us, we have X cubed plus. 125 here, X cubed can be rewritten as X times itself three times. So we can represent this as X to the power of three and 125 can be represented as five times itself three times. So 125 can be rewritten as five to the power of three here we can allow A to B X and B two B five and notice that in the original expression we are given a plus sign. So we're trying to factor a sum of cube numbers. So we're going to be using the general rule for factoring a sum of cube numbers. So we already have our A and B values. We just need to go ahead and plug this into the general rule and that's going to give us A plus B which is X plus five times a squared which is X squared minus eight times B which is X times five plus B squared which is five squared Now five times X is going to give us five x and five squared is going to give us 25. So simplifying this is going to give us X plus five times the quantity X squared minus five X plus 25. And this is going to be the completely factored version of our original expression and that means that the answer to this problem is going to be be So I hope this video helps you in understanding how to factor a sum of cube numbers and I'll go ahead and see you all in the next video

In Exercises 57–64, factor using the formula for the sum or difference of two cubes. x^3+64

Key Concepts

Sum of Cubes Formula

Identifying a and b

Factoring Process

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